A novel structural reliability analysis method combining the improved beluga whale optimization and the arctangent function‐based maximum entropy method

Abstract

A novel structural reliability analysis method that combines the improved beluga whale optimization (IBWO) and the arctangent function‐based maximum entropy method (AMEM) is proposed in this paper. It aims to augment the accuracy of failure probability prediction in structural reliability analysis based on the traditional maximum entropy method (MEM). First, the arctangent function is introduced to avoid the effects of truncation error and numerical overflow in the traditional MEM. The arctangent function can nonlinearly transform the structural performance function defined on the infinite interval into a transformed performance function defined on the bounded interval. Subsequently, the undetermined Lagrange multipliers in the maximum entropy probability density function (MEPDF) of the transformed performance function are obtained using IBWO at a swifter convergence speed with heightened convergence accuracy. Finally, the MEPDF of the transformed performance function can be obtained by combining the IBWO and AMEM, and the structural failure probability can be predicted. The analysis of the metro bogie frame as an engineering example reveals that compared with the traditional MEM using the genetic algorithm to solve the Lagrange multipliers, the proposed method diminishes the relative error in failure probability prediction from 20.51% to only 0.09%. This method significantly enhances the prediction accuracy of failure probability.